Optical system for head-mounted display

ABSTRACT

An optical system for a head-mounted display in which image rays provided from a display device are divergent to form and provide an enlarged image is configured so that first and second lenses are sequentially disposed from an object along an optical axis and provide the enlarged image on an image plane, and angles of principal rays are gradually increased from the optical axis toward the edge of the image plane. Thus, as the angles of principal rays are increased, an angle of view is improved to provide a large screen so that it is possible to appreciate a vivid image due to an increase in the sense of presence and the degree of involvement. The entire size of the optical system can be reduced. The head-mounted display can be made compact and lightweight.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Korean PatentApplication No. 10-2013-0069166 filed in the Korean IntellectualProperty Office on Jun. 17, 2013, the entire contents of which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates, in general, to a head-mounted displayand, more particularly, to an optical system for a head-mounted display,in which lenses are arranged along an optical axis to allow angles ofprincipal rays incident upon an image plane to be gradually increased,thereby increasing an angle of view, reducing a length of the opticalsystem, and increasing the sense of presence and the degree ofinvolvement

2. Description of the Related Art

Generally, a head-mounted display (HMD) refers to a device that is wornon the head of a user, has an optical system embedded therein, andenables the user to enjoy large images in front of his or her eyes.

Particularly, the HMD is realized with both eyes of a user isolated fromhis or her surroundings, is provided therein with optical lenses,enables the user to enjoy images on a considerably wider screen than areal screen, and allows the degree of involvement, the sense ofpresence, and the degree of perception to be further increased.

The HMD has been provided in various shapes such as glasses, a helmet,and a cap. Recently, in consideration of a tendency towardpopularization based on demands of consumers and technical development,in addition to portability and comfort, studies have been actively madeof designs for small-sized, lightweight, and simple and elegant designs.

The basic principle of the HMD places an object within a focal length ofa concave mirror so that an upright virtual image is enlarged and formedbehind the concave mirror, and enables a user to recognize the enlargedvirtual image so as to enjoy the enlarged images.

FIG. 1 schematically shows an optical system provided for a conventionalhead-mounted display.

As shown in FIG. 1, a liquid crystal display (LCD) on which an imageinput outside is displayed is located at one side, and incident light ofthe image is reflected on a half mirror, is incident on an concavemirror, so that a user can appreciate an upright virtual image enlargedbehind the concave mirror.

The prior art using this principle is disclosed in Korean Patent Nos.10-0304622 and 10-0272375, and Korean Unexamined Patent ApplicationPublication No. 10-2005-0005823.

First, in the first technology (Korean Patent No. 10-0304622), anoptical system for a head-mounted display in which an image producedfrom a display device is enlarged and formed by light irradiated by alight source and can be provided to a user, includes an imaging lensunit that has at least one lens formed of a high-refractionhigh-dispersion material and having strong negative power and at leastone lens formed of a low-refraction low-dispersion material and havingpositive power and which condenses the image produced from the displaydevice, a filter lens that has positive power and forms an incidentimage on a primary imaging plane along with the imaging lens unit, ahalf mirror that transmits or reflects incident light to change itspath, and a reflective mirror on which light split and cast from thehalf mirror and which reflects the light toward the eyes of the user.

The second technology (Korean Patent No. 10-0272375) includes an opticalimage generating means of irradiating image information input from theoutside, a reflecting and transmitting means of reflecting andtransmitting an optical image from the optical image generating means,and a virtual image forming means of forming the optical image reflectedby the reflecting and transmitting means into an upright virtual imageand being asymmetrically installed at a position corresponding to thereflecting and transmitting means.

Finally, in the third technology (Korean Unexamined Patent ApplicationPublication No. 10-2005-0005823), an optical system for a head-mounteddisplay that enlarges image light output from a predetermined displaydevice at a predetermined magnification and produces large images atpositions adjacent to both eyes includes a spontaneously emitted singlelight emitting display device for outputting predetermined image light,an X-prism equalizing the image light output from the light emittingdisplay device, a pair of relay lens systems that enlarge, converge, andtransfer each image light split and refracted by a reflective plane ofthe X-prism at a predetermined magnification, and a pair of reflectivemirrors that are disposed adjacent to the left and right eyes of a userat a predetermined reflective angle so as to be able to convert andreflect the image light enlarged and converged by each relay lens systemtoward the left and right eyes.

Each of the prior arts includes the optical system for the HMD thatenlarges the image produced from the display device and provides theenlarged image to the user. The optical systems have the half mirror andthe reflective mirror as the common components.

Fundamentally, the half mirror should be located at a focal point formedby the reflective mirror. If this structure is not provided, variousimaging lens units and relay lens systems should be introduced, and theimage of the display device should be located at or inside the focus ofthe reflective mirror.

That is, the light reflected by the half mirror is enlarged on theentire plane of the reflective mirror so that an upright virtual imageis formed. This structure can be miniaturized when a small displaydevice having a size of 25 mm or less is used. However, a small displaydevice has a disadvantage in that it is expensive if its resolution isincreased. When an inexpensive and low-resolution display device isused, there is a limit in that the size of the HMD can be no longerreduced.

This imposes restrictions on realizing portability or miniaturizationand is problematic in realizing a reduction in weight. This weightcauses fatigue when the user wears the HMD on the head for a long time.

Further, the optical system for the HMD having such a structuregenerally has an angle of view of about 30 to 50 degrees, and thusreduces enlarging capability and creates difficulty providing a largeimage having a predetermined magnification. This can be overcome byreducing the radius of curvature of the reflective mirror. However, todo so, the half mirror should be disposed adjacent to the reflectivemirror. In this case, the light path is interrupted, and thus it isdifficult to provide a large image having a predetermined magnification.

FIG. 2 schematically shows an optical system using a principle of amagnifier among the conventional optical systems for the HMD. Thisstructure can realize a large image using a display device having a sizeof 30 mm or more without using a small display device. However, a lenshas a larger size than the display device, and thus the system has avery large size and is increased in weight. Thus, there is adisadvantage in that it is inconvenient to wear the HMD.

SUMMARY OF THE INVENTION

Accordingly, the present invention has been made keeping in mind theabove problems occurring in the related art, and the present inventionis intended to propose an optical system for a head-mounted display, inwhich lenses are arranged along an optical axis to allow angles ofprincipal rays incident upon an image plane to be gradually increased,thereby increasing an angle of view, reducing a size of the opticalsystem so as to be easily worn, and increasing the sense of presence andthe degree of involvement.

In order to achieve the above object, according to one aspect of thepresent invention, there is provided an optical system for ahead-mounted display, in which image rays provided from a display deviceare divergent to provide an enlarged image. First and second lenses aresequentially disposed along an optical axis so as to allow angles ofprincipal rays incident upon an image plane to be gradually increasedfrom an optical axis toward an edge of the image plane. The first lenshas positive refractive power, and the second lens has negativerefractive power. |R1/R2|>2.5, and |f1/f2|<0.6, where R1 is a radius ofcurvature of a front surface of the first lens, R2 is a radius ofcurvature of a rear surface of the first lens, f1 is a focal length ofthe first lens, and f2 is a focal length of the second lens.

Here, the principal rays may be configured so that the angles thereofare gradually increased between 20% and 80% of a size of the imageformed on the image plane.

Further, the second lens may satisfy a condition of Tc/Te<0.7, where Tcis a thickness in the middle of the second lens, and Te is a thicknessat a position corresponding to 70% of an effective diameter of thesecond lens.

Also, the first and second lenses may be formed of different materials.The first and second lenses may be separately formed and have at leastone aspheric surface.

According to the present invention, as the angles of principal rays areincreased, the angle of view is improved to provide a large screen, andresolution is increased, so that it is possible to appreciate a vividimage due to an increase in the sense of presence and the degree ofinvolvement.

Further, the optical system allows its entire size to be reduced whilesecuring a predetermined angle of view. Thus, the head-mounted displaycan be made compact and lightweight. Accordingly, head-mounted displaysof simple and elegant designs can be supplied according to demands ofvarious consumers along with improvements in portability and comfort.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more clearly understood from the following detaileddescription when taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 schematically shows an optical system provided for a conventionalhead-mounted display (HMD);

FIG. 2 schematically shows an optical system using a principle of amagnifier among the conventional optical systems for the HMD;

FIG. 3 shows an optical system for an HMD in accordance with a firstembodiment of the present invention;

FIG. 4 shows an optical system for an HMD in accordance with a secondembodiment of the present invention; and

FIG. 5 shows an optical system for an HMD in accordance with a thirdembodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed to an optical system for ahead-mounted display (HMD) worn on the head of a user, in which imagerays provided from a display device are divergent to allow an enlargedimage to be formed and provided to both eyes of the user, and in whichfirst and second lenses are disposed from an object along an opticalaxis in that order and provide the enlarged image.

Reference will now be made in greater detail to exemplary embodiments ofthe invention with reference to the accompanying drawings.

The optical system for the HMD according to the present inventionincludes lenses enlarging a small image provided from the displaydevice, and is basically designed so as to use the position of an eye asan entrance pupil and a position of the display device as an imageplane.

That is, when the lens is viewed through the user's eye located at theentrance pupil, a virtual image is formed on the image plane behind thelens. A size of the virtual image formed on the image plane becomes thesize of a screen actually recognized by the user.

To realize the optical system for the HMD according to the presentinvention in this way, the first and second lenses are disposed from theobject along the optical axis in that order and provide the enlargedimage. Angles of principal rays incident upon the image plane aregradually increased from the optical axis toward the edge of the imageplane.

Here, the principal rays refer to rays passing through a stop. The lastray left in a process of reducing the stop is representative of aluminous flux. Aberrations such as astigmatism, a curvature of imagefield, distortion are obtained with respect to the principal rays. Inthe present invention, the angles of principal rays incident upon theimage plane are gradually increased with the approach to the edge of theimage plane.

The fact that the angles of principal rays are increased means that itis possible to reduce a total length of the optical system in which thelenses are included in the HMD and to increase an angle of view.

In general, when the angle of view is increased, the image can beenlarged at a high magnification. However, the image is subjected tosevere distortion and a decrease in resolution, and the size of theoptical system is increased.

However, when the optical system for the HMD according to the presentinvention is used, the angles of principal rays are increased to allowthe principal rays to uniformly arrive up to the edge of the imageplane. Thus, the angle of view can be increased, and the image can beenlarged at a high magnification. Nevertheless, an image a having highresolution and a large size is provided without severe distortion.

In this way, when the optical system for the HMD according to thepresent invention is used, the angle of view is equal to or greater than70°. This provides only the enlarged image having the angle of view of70° or more in a state in which a peripheral field of view is isolated,so that it is possible to realize a remarkable increase in the sense ofpresence and the degree of involvement.

Above all, the present invention is designed so that the angles of theprincipal rays are gradually increased within an area that occupies 20to 80% of the size of the image formed on the image plane. In detail,since the angles of the principal rays are slightly increased within anarea of 0 to 20%, the degree of distortion is weak. Since an area of 80%or more is an edge of the image plane, the distortion is not noticeablyrecognized although it is not corrected.

Meanwhile, a total of two lenses are used in the optical system for theHMD according to the present invention. That is, the first and secondlenses are sequentially disposed from the object along the optical axisand provide the enlarged image.

Here, it is preferable that the first lens has positive refractivepower, and the second lens has negative refractive power.

Further, a ratio of the radius of curvature R1 of a front surface of thefirst lens to the radius of curvature R2 of a rear surface of the firstlens is preferably less than 2.5 (|R1/R2|<2.5), i.e., the radius ofcurvature R1 of the front surface of the first lens is preferablygreater than the radius of curvature R2 of the rear surface of the firstlens.

Further, a ratio of a focal length f1 of the first lens to a focallength f2 of the second lens is preferably less than 0.6 (|f1/f2|<0.6).

In addition, it is preferable that the first and second lenses areformed of different materials, are separately formed, and have at leastone aspheric surface.

To correct the aberrations of the first lens, it is favorable that theratio of the radius of curvature of the front surface to the radius ofcurvature of the rear surface is satisfied as described above. Further,to correct the aberrations, it is favorable that the second lens hasweak negative refractive power and the first lens has strong positiverefractive power. To do so, it is favorable that the ratio of the focallength of the first lens to the focal length of the second lenssatisfies the aforementioned condition. The shape and material for thefirst and second lenses are conditions that minimize sphericalaberrations such as coma aberration, a curvature of image field, anddistortion aberration and chromatic aberration to enhance performance ofthe optical system and can reduce the entire size of the optical system.

Further, the second lens is designed to have weak negative refractivepower in the middle thereof compared to the other portion and to havestrong negative refractive power with the approach to the edge thereof,thereby gradually increasing the angles of the principal rays to reducethe length and the distortion aberration of the optical system. In thiscase, it is favorable that the second lens satisfies the condition thata ratio of a thickness Tc in the middle to a thickness Te at a positioncorresponding to 70% of an effective diameter is less than 0.6(Tc/Te<0.6).

In this way, the optical system according to the present invention hasthe positive refractive power as a whole. To correct the aberrations,the first lens has the strong positive refractive power, and the secondlens has the weak negative refractive power. Thereby, the angles of theprincipal rays are gradually increased to be able to provide the imageof high magnification.

Hereinafter, exemplary embodiments of the present invention will bedescribed.

First Embodiment

FIG. 3 shows an optical system for an HMD in accordance with a firstembodiment of the present invention.

As shown, a first lens L1 and a second lens L2 are sequentially arrangedfrom the object along an optical axis. Here, the object is a virtualobject and refers to a distance from an enlarged image when a userdirectly recognizes the enlarged image.

Numerical data of the lenses constituting the optical system accordingto the first embodiment of the present invention are shown in Table 1below.

TABLE 1 Radius of Refractive Abbe curvature Thickness index value PlaneNo. (RDY) (THI) (Nd) (Vd) OBJ INFINITY 2000 STO INFINITY 11 2 71.48112.31 1.531 55.8 3 −18.674 0.43 4 56.509 1.70 1.585 30.0 5 25.087 39.57IMG INFINITY 0 (OBJ: Object plane, STO: Stop, IMG: Image plane, andInfinity: Flat plane)

As shown in FIG. 3, the stop STO is disposed at the side of the object,and the first lens L1 and the second lens L2 are disposed from the stop.When an optical axis direction is set as X, and a directionperpendicular to the optical axis is set as a Y axis, an asphericformula is as follows:

Formula 1

${X(Y)} = {{\frac{Y^{2}}{R}\frac{1}{1 + \sqrt{1 - {\left( {1 + K} \right)\left( \frac{Y}{R} \right)^{2}}}}} + {AY}^{4} + {BY}^{6} + {CY}^{8} + {DY}^{10} + {EY}^{12} + {FY}^{14}}$

An aspheric surface is a curved surface obtained by rotating a curveobtained by Formula 1 round the optical axis. In Formula 1, R is theradius of curvature, K is the conic constant, and A, B, C, D, E, and Fare the aspheric coefficients.

The aspheric coefficients of Formula 1 which are derived from the dataof the lenses are given as in Table 1 below.

TABLE 2 A B C D E F S2 −3.67054E−05 −7.44523E−08   6.48080E−10−1.99642E−12   7.69976E−15 −1.16220E−17 S3 −5.95035E−07 −1.16964E−07  7.58065E−10 −4.54880E−13 −7.51177E−15   2.53831E−17 S4 −7.12688E−05  2.59311E−07 −3.31290E−10   5.71877E−14   4.44975E−17   9.77508E−20 S5−4.93594E−05   1.32441E−07 −2.09467E−10 −8.78022E−14   5.54735E−16−5.15126E−19

The angle of view, the height of image, and the incident angle of theimage plane 10 of the principal rays in the optical system having theselenses are shown in Table 3 below.

TABLE 3 Angle Height of Angle of of view image principal ray (°) (mm)(°) 0.0 0 0 4.5 3.48 3.20 9.0 7.02 6.10 13.5 10.68 8.43 18.0 14.48 10.0222.5 18.43 10.91 27.0 22.55 11.39 31.5 26.90 12.07 36.0 31.58 13.92 40.536.70 18.13 45.0 42.00 25.61

As shown in Table 3, it can be found that the angles of the principalrays are gradually increased. In particular, it can be confirmed thatthere is a distinct phenomenon in which the angles of the principal raysare gradually increased between 20% and 80% with respect to the size ofthe image formed on the image plane 10, i.e. an overall image height of42 mm. It is shown that the angle of view is about 45° (90° includingthe lower half of the optical axis).

In the present embodiment, the first lens has a focal length of 29.27 mmand strong positive refractive power, and the second lens has a focallength of −78.7 mm and weak negative refractive power. A ratio of thefocal length f1 of the first lens to the focal length f2 of the secondlens is 0.37 (|f1/f2|=0.37).

Further, in the first lens, a ratio of the radius of curvature R1 of thefront surface to the radius of curvature R2 of the rear surface is 3.83(|R1/R2|=3.83).

Also, in the second lens, a thickness Tc in the middle is 1.7 mm, and athickness Te at a position corresponding to 70% of an effective diameteris 4.86 mm. A ratio of the thickness Tc to the thickness Te is 0.35(Tc/Te=0.35).

In addition, the first and second lenses are formed of differentmaterials, are separately formed, and have both aspheric surfaces.

In this way, due to the gradual increase of the angles of the principalrays, the angle of view is increased. Due to this effect, the opticalsystem can be designed for its entire size of about 55 mm, and the HMDcan be made compact and lightweight. Due to the increase of the angle ofview, the sense of presence and the degree of involvement are increased.

Second Embodiment

FIG. 4 shows an optical system for an HMD in accordance with a secondembodiment of the present invention.

As shown, a first lens L1 and a second lens L2 are sequentially arrangedfrom the object along an optical axis. Here, the object is a virtualobject and refers to a distance from an enlarged image when a userdirectly recognizes the enlarged image.

Numerical data of the lenses constituting the optical system accordingto the second embodiment of the present invention are shown in Table 4below.

TABLE 4 Radius of Thick- Refractive Abbe curvature ness index valuePlane No. (RDY) (THI) (Nd) (Vd) OBJ INFINITY 2000 STO INFINITY 10 267.054 11.18 1.531 55.8 3 −20.675 0.20 4 49.507 1.80 1.585 30.0 5 22.83441.82 IMG INFINITY 0 (OBJ: Object plane, STO: Stop, IMG: Image plane,and Infinity: Flat plane)

As shown in FIG. 4, the stop STO is disposed at the side of the object,and the first lens L1 and the second lens L2 are disposed from the stop.When an optical axis direction is set as X, and a directionperpendicular to the optical axis is set as a Y axis, an asphericformula is given as in Formula 1.

The aspheric coefficients of Formula 1 which are derived from the dataof the lenses are given as in Table 5 below.

TABLE 5 A B C D E F S2   3.40429E−06 −3.02420E−07   1.27810E−09−1.97775E−12   2.03720E−15 −1.90049E−18 S3   1.25201E−05 −1.14165E−07  2.61400E−10   8.26441E−13 −4.31929E−15   9.49326E−18 S4 −6.41851E−05  2.41461E−07 −1.85031E−10 −2.75073E−13 −6.61195E−16   1.92626E−18 S5−6.50926E−05   2.63434E−07 −5.30520E−10 −5.75878E−14   1.02349E−15−8.43238E−19

The angle of view, the height of image, and the incident angle of theimage plane 10 of the principal rays in the optical system having theselenses are shown in Table 6 below.

TABLE 6 Angle Height Angle of of view of image principal ray (°) (mm)(°) 0 0.00 0.00 5 4.18 1.03 10 8.42 2.06 15 12.79 3.11 20 17.34 4.27 2522.14 5.65 29 26.24 6.99 32 29.54 8.16 35 33.13 9.45 38 37.10 10.81 4141.60 12.11

As shown in Table 6, it can be found that the angles of the principalrays are gradually increased. In particular, it can be confirmed thatthere is a distinct phenomenon in which the angles of the principal raysare gradually increased between 20% and 80% with respect to the size ofthe image formed on the image plane 10, i.e. an overall image height of41.6 mm. It is shown that the angle of view is about 42° (84° includingthe lower half of the optical axis).

In the present embodiment, the first lens has a focal length of 31.14 mmand strong positive refractive power, and the second lens has a focallength of 74.3 mm and weak negative refractive power. A ratio of thefocal length f1 of the first lens to the focal length f2 of the secondlens is 0.42 (|f1/f2|=0.42).

Further, in the first lens, the ratio of the radius of curvature R1 ofthe front surface to the radius of curvature R2 of the rear surface is3.24 (|R1/R2|=3.24).

Also, in the second lens, a thickness Tc in the middle is 1.8 mm, and athickness Te at a position corresponding to 70% of an effective diameteris 4.32 mm. A ratio of the thickness Tc to the thickness Te is 0.42(Tc/Te=0.42).

In addition, the first and second lenses are formed of differentmaterials, are separately formed, and have both aspheric surfaces.

In this way, due to the gradual increase of the angles of the principalrays, the angle of view is increased. Due to this effect, the opticalsystem can be designed with an entire size of about 55 mm, and thus theHMD can be made compact and lightweight. Due to the increase of theangle of view, the sense of presence and the degree of involvement areincreased.

Third Embodiment

FIG. 5 shows an optical system for an HMD in accordance with a thirdembodiment of the present invention.

As shown, a first lens L1 and a second lens L2 are sequentially arrangedfrom the object along an optical axis. Here, the object is a virtualobject and refers to a distance from an enlarged image when a userdirectly recognizes the enlarged image.

Numerical data of the lenses constituting the optical system accordingto the third embodiment of the present invention are shown in Table 7below.

TABLE 7 Radius of Thick- Refractive Abbe curvature ness index valuePlane No. (RDY) (THI) (Nd) (Vd) OBJ INFINITY 2000 STO INFINITY 10 2117.595 14.41 1.531 55.8 3 −20.644 3.50 4 42.921 1.80 1.585 30 5 26.60635.29 IMG INFINITY 0 (OBJ: Object plane, STO: Stop, IMG: Image plane,and Infinity: Flat plane)

As shown in FIG. 5, the stop STO is disposed at the side of the object,and the first lens L1 and the second lens L2 are disposed from the stop.When an optical axis direction is set as X, and a directionperpendicular to the optical axis is set as a Y axis, an asphericformula is given as in Formula 1.

The aspheric coefficients of Formula 1 which are derived from the dataof the lenses are given as in Table 8 below.

TABLE 8 A B C D E F S2   6.22821E−06 −2.20830E−07   8.95590E−10−1.94639E−12   2.94488E−15 −1.90379E−18 S3   4.29981E−06 −1.04861E−07  1.87839E−10   8.21400E−13 −4.96590E−15   9.82459E−18 S4 −1.73387E−04  3.29816E−07 −6.26003E−12 −1.13393E−13 −8.12726E−16   9.25148E−19 S5−1.61271E−04   4.51185E−07 −5.28657E−10 −1.57306E−13   9.41390E−16−6.79097E−19

The angle of view, the height of image, and the incident angle of theimage plane 10 of the principal rays in the optical system having theselenses are shown in Table 9 below.

TABLE 9 Angle Height of Angle of of view image principal ray (°) (mm)(°) 0 0 0 5 3.81 1.48 10 7.70 2.98 15 11.72 4.55 20 15.87 6.34 25 20.128.47 30 24.43 11.06 35 28.82 14.06 40 33.31 17.24 45 37.83 20.07 5042.00 21.36

As shown in Table 9, it can be found that the angles of the principalrays are gradually increased. In particular, it can be confirmed thatthere is a distinct phenomenon in which the angles of the principal raysare gradually increased between 20% and 80% with respect to the size ofthe image formed on the image plane 10, i.e. an overall image height of42 mm. It is shown that the angle of view is about 50° (100° includingthe lower half of the optical axis).

In the present embodiment, the first lens has a focal length of 34.31 mmand strong positive refractive power, and the second lens has a focallength of 124.74 mm and weak negative refractive power. The ratio of thefocal length f1 of the first lens to the focal length f2 of the secondlens is 0.28 (|f1/f2|=0.28).

Further, in the first lens, the ratio of the radius of curvature R1 ofthe front surface to the radius of curvature R2 of the rear surface is5.7 (|R1/R2|=5.7).

Also, in the second lens, the thickness Tc in the middle is 1.8 mm, andthe thickness Te at a position corresponding to 70% of an effectivediameter is 5.69 mm. The ratio of the thickness Tc to the thickness Teis 0.32 (Tc/Te=0.32).

In addition, the first and second lenses are formed of differentmaterials, are separately formed, and have both aspheric surfaces.

In this way, due to the gradual increase of the angles of the principalrays, the angle of view is increased. Due to this effect, the opticalsystem can be designed with an entire size of about 55 mm, and the HMDcan be made compact and lightweight. Due to the increase of the angle ofview, the sense of presence and the degree of involvement are increased.

When the optical system for the HMD realized by each embodiment of thepresent invention is used, the angle of view can be realized up to about110° due to the increase of the angles of the principal rays. A largescreen of 130 inches or more can be realized at a virtual distance ofabout 2 meters, and thus a vivid image can be appreciated due to theincrease of the sense of presence and the degree of involvement.

Further, the entire size of the optical system can be realized whilebeing equal to or less than 60 mm while securing a predetermined angleof view. Thus, the HMD can be made compact and lightweight. Accordingly,an HMD of simple and elegant designs can be supplied according todemands of various consumers along with the improvement of portabilityand comfort.

Although exemplary embodiments of the present invention have beendescribed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible, without departing from the scope and spirit of the inventionas disclosed in the accompanying claims.

What is claimed is:
 1. An optical system for a head-mounted display, inwhich image rays provided from a display device are divergent to providean enlarged image, wherein first and second lenses are sequentiallydisposed along an optical axis so as to allow angles of principal raysincident upon an image plane to be gradually increased from an opticalaxis toward an edge of the image plane, the first lens has positiverefractive power, and the second lens has negative refractive power,|R1/R2|>2.5, and|f1/f2|<0.6, where R1 is a radius of curvature of a front surface of thefirst lens, R2 is a radius of curvature of a rear surface of the firstlens, f1 is a focal length of the first lens, and f2 is a focal lengthof the second lens.
 2. The optical system according to claim 1, whereinthe principal rays are configured so that the angles thereof aregradually increased between 20% and 80% of a size of the image formed onthe image plane.
 3. The optical system according to claim 1, wherein thesecond lens satisfies a condition of Tc/Te<0.7, where Tc is a thicknessin the middle of the second lens, and Te is a thickness at a positioncorresponding to 70% of an effective diameter of the second lens.
 4. Theoptical system according to claim 1, wherein the first and second lensesare formed of different materials.
 5. The optical system according toclaim 4, wherein one of the first and second lenses is formed ofplastic.
 6. The optical system according to claim 1, wherein the firstand second lenses are separately formed and have at least one asphericsurface.
 7. The optical system according to any one of claims 1 to 6,wherein the optical system has an angle of view of 65° or more.
 8. Anoptical system for a head-mounted display, in which image rays providedfrom a display device are divergent to provide an enlarged image,wherein first and second lenses are sequentially disposed along anoptical axis so as to allow angles of principal rays incident upon animage plane to be gradually increased from an optical axis toward anedge of the image plane between 20% and 80% of a size of the imageformed on the image plane, the first lens has positive refractive power,and the second lens has negative refractive power,|R1/R2|>2.5, and|f1/f2|<0.6, where R1 is a radius of curvature of a front surface of thefirst lens, R2 is a radius of curvature of a rear surface of the firstlens, f1 is a focal length of the first lens, and f2 is a focal lengthof the second lens.
 9. The optical system according to claim 8, whereinthe second lens satisfies a condition of Tc/Te<0.7, where Tc is athickness in the middle of the second lens, and Te is a thickness at aposition corresponding to 70% of an effective diameter of the secondlens.
 10. The optical system according to claim 8, wherein the first andsecond lenses are formed of different materials.
 11. The optical systemaccording to claim 10, wherein one of the first and second lenses isformed of plastic.
 12. The optical system according to claim 8, whereinthe first and second lenses are separately formed and have at least oneaspheric surface.
 13. The optical system according to any one of claims8 to 12, wherein the optical system has an angle of view of 65° or more.